Binomial Theorem, Sequences and Series One Mark Question

11th Standard

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Maths

Time : 00:30:00 Hrs
Total Marks : 10
    10 x 1 = 10
  1. If a, 8, b are in AP, a, 4, b are in GP, and if a, x, b are in HP then x is

    (a)

    2

    (b)

    1

    (c)

    4

    (d)

    16

  2. The HM of two positive numbers whose AM and GM are 16,8 respectively is

    (a)

    10

    (b)

    6

    (c)

    5

    (d)

    4

  3. The nth term of the sequence 1, 2, 4, 7, 11,... is

    (a)

    n3+3n2+2n

    (b)

    n3-3n2+3n

    (c)

    \(\frac { n(n+1)(n+2) }{ 3 } \)

    (d)

    \(\frac { { n }^{ 2 }-n+2 }{ 2 } \)

  4. The sum of an infinite GP is 18. If the first term is 6, the common ratio is

    (a)

    \(\frac { 1 }{ 3 } \)

    (b)

    \(\frac { 2 }{ 3 } \)

    (c)

    \(\frac { 1 }{ 6 } \)

    (d)

    \(\frac { 3 }{ 4 } \)

  5. If the sum of n terms of an A. P. be 3n2 - n and its common difference is 6, then its first term is

    (a)

    2

    (b)

    3

    (c)

    1

    (d)

    4

  6. The term without x in \({ \left( 2x-\frac { 1 }{ 2{ x }^{ 2 } } \right) }^{ 12 }\) is 

    (a)

    495

    (b)

    -495

    (c)

    -7920

    (d)

    7920

  7. The first and last term of an A.P.are 1 and 11.If the sum of its terms is 36, then the number of terms will be

    (a)

    5

    (b)

    6

    (c)

    7

    (d)

    8

  8. If in an infinite G. P., first term is equal to 10 times the sum of all successive terms, then its common ratio is

    (a)

    \(\frac { 1 }{ 10 } \)

    (b)

    \(\frac { 1 }{ 11 } \)

    (c)

    \(\frac { 1 }{ 9 } \)

    (d)

    \(\frac { 1 }{ 20 } \)

  9. The nth term of a G. Pis 128 and the sum of its n terms is 225. If its common ratio is 2, then its first term is

    (a)

    1

    (b)

    3

    (c)

    8

    (d)

    none of these 

  10. The value of \({ 9 }^{ \frac { 1 }{ 3 } }\) ,\({ 9 }^{ \frac { 1 }{ 9 } }\)\({ 9 }^{ \frac { 1 }{ 27 } }\) ,\(\infty \)is

    (a)

    1

    (b)

    3

    (c)

    9

    (d)

    none of these

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